Colour level set regularization for the electromagnetic imaging of highly discontinuous parameters in 3D*

In this paper, we propose a novel reconstruction scheme for the low-frequency near-field electromagnetic imaging of high-contrast conductivity distributions inside shielded regions using the system of Maxwell's equations in 3D. In our novel scheme, we focus on estimating the shape characteristics of the electrical conductivity profile inside these regions from low-frequency electromagnetic data measured at external locations for a single frequency. We introduce a colour level set regularization scheme which is a shape-based approach focusing on the simultaneous reconstruction of several shape-like distributions of different conductivity values in the same region of interest. Using two numerical experiments addressing a three-value reconstruction problem related to the imaging of shielded boxes or cargo containers, we compare this novel approach with results obtained from standard voxel-based reconstruction schemes on the one hand and the more established two-value shape-based approach on the other hand. We demonstrate that, depending on the particular situation of the imaging setup, this three-value (or in general multiple-value) shape-based reconstruction technique has the potential to provide superior reconstruction results in many situations, in particular regarding reconstruction of the correct shapes. We also discuss particular challenges of this novel methodology.